If the objective function \(Z = px + qy, p \gt 0, q \gt 0\) of a linear programming problem attains its optimal value at the points (4, 7) and (5, 5) and \(pq = 50\) then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(p = 10,q=5\)
If the optimal value occurs at both points, Z must take equal values there:
\(4p + 7q = 5p + 5q\)
\(p = 2q\)
With \(pq = 50\):
\(2q \cdot q = 50\)
\(q^2 = 25\)
\(q = 5\) (since \(q \gt 0\)), \(p = 10\)
Every option satisfies \(pq = 50\), so the condition p = 2q is what decides; only Option (2) satisfies it.